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Astron. Astrophys. 325, 685-692 (1997)

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4. The change of [FORMULA] with time

André et al. (1993) suggested the use of the ([FORMULA] / [FORMULA]) ratio as an evolutionary indicator for pre-main-sequence objects because, during this phase, the circumstellar mass, proportional to [FORMULA], is expected to decrease, disappearing when the object reaches the main-sequence. As a consequence of this, older sources will have a higher ([FORMULA] / [FORMULA]) value.

In Fig. 2 we plot the objects of our sample in a ([FORMULA] / [FORMULA]) versus [FORMULA] diagram. We see a trend towards a correlation between the two plotted quantities and the best-fit log([FORMULA] / [FORMULA])= 1.32 [FORMULA] +2.635 (solid line) gives a correlation probability of 95.5%.

[FIGURE] Fig. 2. The bolometric-to-1.3 mm luminosity ratio versus [FORMULA]. The solid line is the best-fit log([FORMULA] / [FORMULA])=1.32 [FORMULA] +2.635, with a 95.5% correlation probability

Fig. 2 also shows that sources with a high value of [FORMULA] / [FORMULA] (older sources) also tend to have a higher [FORMULA] value. Therefore, [FORMULA] seems to increase with time. Dent et al. (1995), using a submillimetre colour-colour diagram, also noted an increase of [FORMULA], associated with an increase in the dust temperature, as the sources evolve. Our sources, superimposed on their diagram (their Fig. 1b), follow the same trend of a colour-colour increase as time proceeds (older sources have higher temperatures and higher [FORMULA], see Table 2). They interpreted the observed evolution as being due to a change in dust properties. A temperature increase during the source evolution can change the dust structure (destruction of ice mantles and compact structures). This agrees with the observed evolution of the dust opacity law (Ossenkopf & Henning 1994), [FORMULA], which changes from [FORMULA] to [FORMULA] (respectively for small silicate grains with a coating of amorphous carbon with an ice mantle, and for small silicate grains with separated amorphous carbon grains). The flatter submillimetre spectrum observed for Class 0 sources (Ward-Thompson et al. 1995) could be interpreted as being due to the presence of larger grains in their envelopes, well expressed by a lower [FORMULA] value (Krügel & Siebenmorgen 1994; Dent et al. 1995).

Another indication of the possible evolution of [FORMULA] is shown in Fig. 3. We have plotted our data in a bolometric luminosity ([FORMULA]) versus millimetre flux ([FORMULA]) diagram (Saraceno et al. 1996). In such a diagram, Saraceno et al. (1996) plotted evolutionary tracks for accreting objects. Each track originates from an envelope of initial mass of dust and gas that produces objects of different masses. The dust temperature and opacity law are fixed (T =25 K, [FORMULA] =1.5; see their Sect. 5.4 for further details). The points on the lines correspond to a constant time step of 104 years.

[FIGURE] Fig. 3. Bolometric luminosity, [FORMULA], versus the 1.3 mm flux, [FORMULA]. Evolution tracks are shown for initial mass envelopes of 1, 2 and 4  [FORMULA] and a constant mass accretion rate of [FORMULA] =10-5   [FORMULA] /year. The first (lowest) points are for 2 104 years. Each subsequent point represents a time step of 104  years

From Fig. 3, we can propose an evolutionary sequence from younger to older sources: VLA1, S11, S32 and S55. The corresponding [FORMULA] increases with time (from 1.25 for VLA1 to 1.68 for S55). Moreover, even if in this scheme objects have different masses, we can say that S22 ([FORMULA] =1.51) is older than VLA1 ([FORMULA] =1.25) and S85 ([FORMULA] =1.21) or that S55 ([FORMULA] =1.68) is older than S59 ([FORMULA] =1.26). This indicates that [FORMULA] may increase with time.

The increase in [FORMULA] produces a steeper slope of the continuum as the source evolves. This shape indirectly influences the determination of the bolometric luminosity, i.e. objects with similar [FORMULA] but with a higher [FORMULA] will have a higher bolometric luminosity (see for example the cases of S22 and S32 or S55 and S85 in Fig. 3). Therefore, the possible evolution of [FORMULA] (traducing a change in dust properties) could influence the increase of the ([FORMULA] / [FORMULA]) ratio.

Two other points give further indications in favour of an evolution of [FORMULA] with time.
Due to their sharply peaked spectral energy distributions, Class I sources of our sample show a proportionality between their 100 µm flux and their bolometric luminosity. Therefore we have


Moreover, using Eq.  1, we can also write


with [FORMULA]. Equations (6) and (7) show that the ([FORMULA] / [FORMULA]) ratio is a function of T and [FORMULA] and we see that [FORMULA] increases with this ratio. As a direct consequence, if we fix the same temperature for all the source and use Eq.  1taking only the submillimetre points, we find [FORMULA] values that also increase with the [FORMULA] / [FORMULA] ratio.
Because as time proceeds the envelope material is dispersed or accreted, the decrease of the 1.3 mm flux is an evolutionary indicator. Using the time sequence seen in Fig. 3, we can make an [FORMULA] - [FORMULA] diagram. On such a diagram, in a given class of mass defined by the intensity of the 1.3 mm flux, the [FORMULA] value (obtained with the least-squares fit) increases as the flux diminishes. This last point also indicates a possible evolution of [FORMULA] as time proceeds.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998